An Australian woman kidnapped with her doctor husband in Burkina Faso by a group affiliated to al-Qaeda has been freed, neighbouring Niger's President Mahamadou Issoufou says.

Issoufou presented Jocelyn Elliott at a news conference in Dosso, southwestern Niger on Saturday and said authorities were intensifying efforts to secure the release of her husband.

West Australian Dr Ken Elliott and his wife, both aged in their 80s, were abducted following attacks in the Burkina Faso capital of Ouagadougou by suspected Islamic extremists on January 15.

Al-Qaeda in the Islamic Maghreb said on Friday it had kidnapped the couple and would release the woman unconditionally due to public pressure and guidance from al-Qaeda leaders not to involve women in war.

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The circumstances of her release and how she arrived in Niger were not immediately clear.

For more than 40 years, Dr Elliott and Mrs Elliott have operated a 120-bed clinic in the town of Djibo near Burkina Faso's border with Mali.

They were abducted from the town the same day al-Qaeda fighters raided a restaurant and hotel in Burkina Faso's capital, Ouagadougou, and killed 30 people, many of whom were foreigners.

The couple's children are desperately hoping their mother's release means their father will also soon be free.

After three weeks in captivity Jocelyn Elliot was overnight presented to the media by Niger's President Mahamadou Issoufou in Dosso, who said authorities were still working to secure Dr Ken Elliott's release.

"We are trusting that the moral and guiding principles of those who have released our mother will also be applied to our elderly father, who has served the community of Djibo and the Sahel for more than half his lifetime," the couple's family said in a statement.

"They are separated now but united in their desire to bring healing and hope to the people of Northern Burkina Faso and the surrounding regions.

"We respectfully request that they be allowed to continue their work together, providing essential surgical services."

-AAP